How do you find the indefinite integral of #int x(5^(-x^2))#? Calculus Introduction to Integration Integrals of Exponential Functions 1 Answer Narad T. · Steve M Dec 12, 2016 The answer is #=-5^(-x^2)/(2ln5)+C# Explanation: We do the integral by substitution Let #u=x^2#, then, #du=2xdx# #intx(5^(-x^2))dx=1/2int(5^(-u))du# Let #v=5^(-u)# #lnv=ln5^(-u)=-u ln5# #v=e^(-u ln5)# Therefore, #intx(5^(-x^2))dx=1/2int(5^(-u))du=1/2inte^(-u ln5)du# #=-e^(-u ln5)/(2ln5) =-5^(-u)/(2ln5)=-5^(-x^2)/(2ln5)+C# Answer link Related questions How do you evaluate the integral #inte^(4x) dx#? How do you evaluate the integral #inte^(-x) dx#? How do you evaluate the integral #int3^(x) dx#? How do you evaluate the integral #int3e^(x)-5e^(2x) dx#? How do you evaluate the integral #int10^(-x) dx#? What is the integral of #e^(x^3)#? What is the integral of #e^(0.5x)#? What is the integral of #e^(2x)#? What is the integral of #e^(7x)#? What is the integral of #2e^(2x)#? See all questions in Integrals of Exponential Functions Impact of this question 1613 views around the world You can reuse this answer Creative Commons License